Complete the square to solve for $x$. $x^{2}-12x+35 = 0$
Explanation: Begin by moving the constant term to the right side of the equation. $x^2 - 12x = -35$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $-12$ , half of it would be $-6$ , and squaring it gives us ${36}$ $x^2 - 12x { + 36} = -35 { + 36}$ We can now rewrite the left side of the equation as a squared term. $( x - 6 )^2 = 1$ Take the square root of both sides. $x - 6 = \pm1$ Isolate $x$ to find the solution(s). $x = 6\pm1$ So the solutions are: $x = 7 \text{ or } x = 5$ We already found the completed square: $( x - 6 )^2 = 1$